We show how we can transform the ${\mathscr{H}}_{\infty }$ and ${\mathscr{H}}_2$ control problems of descriptor systems with invariant zeros on the extended imaginary into problems with state-space systems without such zeros. Then we present necessary and sufficient conditions for existence of solutions of the original problems. Numerical algorithm for ${\mathscr{H}}_{\infty }$ control is given, based on the Nevanlinna-Pick theorem. Also, we present an explicit formula for the optimal ${\mathscr{H}}_2$ controller.